The polynomial $$\(\mathrm{p}(x)\)$$ is defined by $$\[ \mathrm{p}(x)=x^{3}+a x^{2}+b x+16 \]$$ where $$\(a\)$$ and $$\(b\)$$ are constants. It is given that $$\((x+2)\)$$ is a factor of $$\(\mathrm{p}(x)\)$$ and that the remainder is 72 when $$\(\mathrm{p}(x)\)$$ is divided by $$\((x-2)\)$$. Find the values of $$\(a\)$$ and $$\(b\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Answer:

Knowledge points:

Solution: